Quote:
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Originally Posted by jinydu
For example, simplify the following:
cbrt(-54+sqrt(2700))+cbrt(-54-sqrt(2700))
This time, I will not give out the answer a priori (although this particular case was also handpicked carefully). Also, the technique (maybe algorithm is an even better word) you use should also work for:
cbrt(10 + sqrt(108)) + cbrt(10 - sqrt(108))
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I get cbr(-6). Once again if there is a simplified form it must lie
within the maximal order of one of the subfields of Q(alpha) [assuming
a monic polynomial]. Find a basis for the subfield. This gives an expression
for each element within its maximal order. Equate this expression to
your original number and solve for the coefficients.